Formula for Mountain Heights. 443 



We have now to replace p and^' by their values expressed in terms of the ba- 

 rometric observations, viz. /3 and /3'. In so doing, we must make allowance for 

 the difference of the specific gravities of the quicksilver of the barometers at the 

 stations of observation ; at the lower station the specific gravity of the quick- 

 silver is rendered greater than that at the upper station, by the greater power 

 of gravity at the lower station. But the specific gravity of the quicksilver at 

 the upper station is rendered greater than that at the lower station by dimi- 

 nution of temperature. Considering these two totally distinct causes of diffe- 

 rence of specific gravities, if we assume to represent p of the lower station, the 



quantity ^ . — y-j we have to represent p' of the upper station, the quantity 



l+m(r-32) 

 '^l + m{T'-2,-2)' 



^(r + hy- {r + h+ h'-hf (r + h + n y (,_^ H . .^ 



^^^ ) . li- = ? — -,^-V2 — = ^ — 7-^2 = 1 + ~rT = (by omit- 



(r+hy {r + hy (r + hy \ r + hj ^ ■' 



ting quantities too small to be usefully retained) 1 -t- 



2H 



Moreover, l±|il|-^_||l = |1 + ,« (T - 32)\ . \1 + m . {T - 32)|-' 



= S 1 + m (T- 32) I . j 1 - 7?i ( r - 32) -f- Anr + Bm' + Cm^ + &c. j = (by omit- 

 ting second and higher powers of m, as too small to be usefully retained) 

 1 + m (T— T"). Thus we have to replace^ and/)', the expressions 



^('l + ^) and ^'.\l+m{T-T'y. 



Substituting these, we have 



K^ is a function of g, and as g varies with the latitude of the stations of baro- 

 metric observations, it is necessary to consider K^ as a function of the latitude, 

 and to seek its value as such. For this purpose, let K correspond to latitude 

 45°, and let G be corresponding force of gravity, while Ki corresponds to lati- 



